Many bike rental agencies have mountain bikes on their books, so not owning a mountain bike is no excuse.

Cycling on paths and roads in Danish woodland is usually permitted, but in order to protect the woodland and any archaeological remains cycling on the forest floor, on sharp slopes or drystone walls is generally off limits.
The Danish Forest and Nature Agency have prepared a special mountain bike track in Rold Forest where mountain bikers can enjoy themselves without disturbing others or damaging their surroundings. For more information, see the Danish Forest and Nature Agency pamphlet.

If you don’t own a mountain bike you can rent one from a bike rental agency. A day’s rental normally costs between 150 and 200 DKK. Rent bikes from: Rold Skov Cykler

The Danish Mountain Bike Club Dansk Mountainbike website offers further information, (in Danish) about mountain bike riding in Denmark.